It is known that dimerization of .alpha.-methylstyrene under an acidic condition gives 1,1,3-trimethyl-3-phenylindane as a saturated dimer, 2,4-diphenyl-4-methyl-1-pentene and 2,4-diphenyl-4-methyl-2-pentene as unsaturated dimers, and 2,4,6-triphenyl-4,6-dimethyl-1-heptene, etc. as trimers.
Of these oligomers, the unsaturated dimers are useful for their applicability. Known processes for selectively obtaining the unsaturated dimers include dimerization of .alpha.-methylstyrene in the presence of a solid acid, such as activated clay or acid clay, or a cation exchange resin as a catalyst and an approximately equivalent amount of water or a polyhydric alcohol (cf. JP-A-48-44240, the term "JP-A" as used herein means an "unexamined published Japanese patent application"). However, when activated clay or acid clay is mixed with water or a polyhydric alcohol, the catalyst undergoes aggregation due to its high affinity for water or the polyhydric alcohol and fails to function effectively, resulting in a low reaction rate. Additionally, the catalyst tends to aggregate and makes fouling on the wall of the reactor.
A dimerization process for .alpha.-methylstyrene using a solid acid catalyst with a polyethylene glycol monoalkyl ether as a co-catalyst has been proposed (cf. JP-A-63-192727). In this process, a polyethylene glycol monoalkyl ether is used in an amount of from 0.001 to 0.06% by weight based on the starting material. The process has a disadvantage in that the reaction temperature control is practically difficult because of reaction heat.